Some weapons do more than one type of physical damage, like a morningstar (both bludgeoning and piercing) or halberd (both slashing and piercing). Having resistance to only one type will not protect you from the other.

This is usually in addition to a weapon's base damage, or from a spell effect. The most common form of damage resistance is against elemental damage, and spells like endure elements grant resistance to these damage types.

Acid-type damage is, well, acid-type damage. Melf's acid arrow and Acid fog both inflict acid damage. Being damaged by acid does not automatically mean the acid will persist in damaging you over several rounds unless the spell or ability in question specifies that it does damage over several rounds. Extraplanar creatures (like demons and devils) commonly have some resistance to acid. The breath of green dragons, black dragons, and copper dragons are known to be acidic. Acid damage is also frequently associated with assassins due to its corrosiveness.

Cold is the antithesis of fire, and as such, cold damage can be anything from actual ice forming on your skin to damage from freezing. Cone of cold, Ice storm and Ray of frost are spells inflicting cold damage. Resistance to cold damage is common in extraplanar creatures like demons and devils. The breath of white dragons and silver dragons are icy cold and cold damage is often associated with arctic beings and some water based entities.

Electric damage is, well, shocking. The spells most used to bring this effect forth are Call lightning and Lightning Bolt. As with cold and fire, some extraplanar creatures (demons, for example) have resistance to electricity-based damage. The breath of blue dragons and bronze dragons are said to crackle with electricity. Electrical damage is often associated with the element of air.

Fire is your run-of-the-mill fire effect, and incorporates both damage from actual fire as well as damage from heat. Spells involving the element of fire include Fireball and Firebrand. Fire resistance is common in extraplanar creatures like demons and devils. Many creatures like hell hounds, red dragons, and gold dragons can breathe fire and deserts are also associated with fire damage.

Sonic damage is damage inflicted by sound waves. Sound burst is an example of a spell used to bring forth sonic damage. Being deaf does not mitigate sonic damage (however, being silenced does). Sonic damage is relatively uncommon (this applies both ways, as few creatures resist sonic damage), usually associated with traps and Bards.

Magic damage is also known as 'non-elemental damage'. One of the most common spells to deal magic damage is Magic missile. It is very rare for a creature to be resistant to magic damage. Resistance to magic energy should not be confused with spell resistance, however.

In 3.5E D&D, the closest type of damage would be Force damage, as well as "Non-determined" damage done by spells like Disintegrate. Nothing should be able to resist Magic damage.

Negative energy is energy channelled from the negative energy plane and is associated with death and destruction. It deals damage depending on the target's status: If the target is a living creature, it will inflict damage. If the target is an undead creature, however, it will heal the creature. Negative energy is also used to drain levels and ability scores. Spells such as vampiric touch and inflict light wounds deal negative energy damage.

Positive energy is the opposite of negative energy, and is channelled from the positive energy plane. Healing spells such as cure light wounds are its most famous manifestation as the positive energy will heal a living target while damaging an undead one.